Finite Group Databasebeta

← C2×#19146482 #25973004

Subgroups — C2×#19146482 #25973004

Order 11008.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic, complemented
2#19146482C2116yesmaximal, direct product factor
3C2×#14583253C211yesmaximal, characteristic, complemented
4C2×#14583237C211yesmaximal, characteristic, complemented
5C2×#14583210C211yesmaximal, characteristic, complemented
6C2×#14583206C211yesmaximal, characteristic, complemented
7C2×#14583138C211yesmaximal, characteristic, complemented
8C2×#14583126C211yesmaximal, characteristic, complemented
9C2×#14583118C211yesmaximal, characteristic, complemented
10C2×#14583061C211yesmaximal, characteristic, complemented
11C2×#14583055C211yesmaximal, characteristic, complemented
12C2×C4×#10621885C211yesmaximal, characteristic, complemented
13C2×D4×C43⋊C8C211yesmaximal, characteristic, complemented
14C2×#14582895C211yesmaximal, characteristic, complemented
15C22×#13063249C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21C23×C43⋊C8C2211yescharacteristic
22#14583589—24no—
23#14583589C2218yescomplemented
24C2×#13063318—21no—
25C2×#13063317C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063306—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063304C2211yescharacteristic
30C2×C4×Dic86C2211yescharacteristic
31C2×#13063284C2211yescharacteristic
32C2×#13063281—21no—
33C22×C4⋊Dic43C2211yescharacteristic
34#14583253C2218yescomplemented
35#14583237C2218yescomplemented
36#14583210C2218yescomplemented
37#14583206C2218yescomplemented
38#14583138C2218yescomplemented
39#14583126C2218yescomplemented
40#14583118C2218yescomplemented
41#14583061C2218yescomplemented
42#14583055C2218yescomplemented
43C4×#10621885C2218yescomplemented
44D4×C43⋊C8C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49#14582895C2218yescomplemented
50C2×#13063249C2211yescharacteristic
51C2×#13063249C2211yescharacteristic
52C2×#13063249C2211yescharacteristic
53C2×#13063249C2211yescharacteristic
54C2×#13063249C2211yescharacteristic
55C2×#13063249C2211yescharacteristic
56C2×#13063249C2218yescomplemented
57C2×#13063248C2211yescharacteristic
58C2×#13063246C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063246C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C22×#41×C43C2211yescharacteristic
65C23×Q8×C43C2211yescharacteristic
66C43×#548—24no—
67C43×#548C2218yes—
68C2×#124×C43—21no—
69C2×#124×C43C2211yescharacteristic
70C2×C22⋊Q8×C43—21no—
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×#121×C43—21no—
73C2×#121×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C2×C4×D4×C43—21no—
76C2×C4×D4×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C23×Dic43—21no—
79C2×#10621885—24no—
80C2×#10621885—42no—
81C2×#10621885C2314yes—
82C2×#10621885C2314yes—
83C2×#10621883—42no—
84C2×#10621883C2314yes—
85C22×C43⋊C8—42no—
86C22×C43⋊C8—42no—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2314yes—
92C22×C43⋊C8C2314yes—
93#13063318—28no—
94#13063317—22no—
95#13063317C2314yes—
96#13063315—28no—
97#13063306—28no—
98#13063304—22no—
99#13063304—22no—
100#13063304C2314yes—
101#13063304C2314yes—
102C4×Dic86—22no—
103C4×Dic86C2314yes—
104#13063284—22no—
105#13063284C2314yes—
106#13063281—28no—
107C2×C4⋊Dic43—22no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43C2314yes—
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×C4⋊Dic43C2311yescharacteristic
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4—21no—
117C2×Dic43⋊C4—21no—
118C2×C22⋊Dic43—21no—
119C2×C22⋊Dic43—21no—
120C2×C22⋊Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123#13063258C2314yes—
124#13063258C2314yes—
125#13063256C2314yes—
126C4⋊(C43⋊C8)C2314yes—
127#13063249C2314yes—
128#13063249C2314yes—
129#13063249C2314yes—
130#13063249C2314yes—
131#13063249C2314yes—
132#13063249C2314yes—
133#13063248C2314yes—
134#13063246C2314yes—
135#13063246C2314yes—
136#13063246C2314yes—
137C22⋊(C43⋊C8)C2314yes—
138C22⋊(C43⋊C8)C2314yes—
139C4×C43⋊C8C2314yes—
140C2×#41×C43—22no—
141C2×#41×C43—24no—
142C2×#41×C43—42no—
143C2×#41×C43C2314yes—
144C22×Q8×C43—21no—
145C22×Q8×C43—22no—
146C22×Q8×C43—24no—
147C22×Q8×C43—42no—
148C22×Q8×C43C2311yescharacteristic
149C22×Q8×C43C2314yes—
150C22×Q8×C43C2311yescharacteristic
151C22×D4×C43—21no—
152C22×D4×C43—21no—
153C22×D4×C43D411yescharacteristic
154C22×D4×C43C2311yescharacteristic
155C23×C4×C43—21no—
156C23×C4×C43—21no—
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159#124×C43—28no—
160#124×C43—22no—
161#124×C43C2314yes—
162C22⋊Q8×C43—22no—
163C22⋊Q8×C43—28no—
164C22⋊Q8×C43C2314yes—
165#121×C43—28no—
166#121×C43—22no—
167#121×C43C2314yes—
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×D4×C43—28no—
171C4×D4×C43D414yes—
172C4×D4×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43D411yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C22⋊C4×C43D411yescharacteristic
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C24×C43C2×D411yescharacteristic
188#41×C43—28no—
189#41×C43—44no—
190#41×C43—48no—
191C2×Q8×C43—21no—
192C2×Q8×C43—24no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—28no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—44no—
199C2×Q8×C43—44no—
200C2×Q8×C43—48no—
201C2×Q8×C43#4114yes—
202C2×Q8×C43C2412yes—
203C2×Q8×C43C2412yes—
204C2×D4×C43—21no—
205C2×D4×C43—24no—
206C2×D4×C43—24no—
207C2×D4×C43—24no—
208C2×D4×C43—22no—
209C2×D4×C43—22no—
210C2×D4×C43—44no—
211C2×D4×C43—44no—
212C2×D4×C43C2×D414yes—
213C2×D4×C43C2412yes—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—24no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—24no—
223C22×C4×C43—44no—
224C22×C4×C43—44no—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2412yes—
232C22×C4×C43C2412yes—
233C22×C4×C43C2411yescharacteristic
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—24no—
239C22×Dic43—44no—
240C2×Dic86—22no—
241C2×Dic86—22no—
242C2×Dic86—21no—
243C2×Dic86C2412yes—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C2×D414yes—
248C4⋊C4×C43C2412yes—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C22⋊C4×C43C2×D414yes—
254C22⋊C4×C43C2×D414yes—
255C42×C43—24no—
256C42×C43C2×D412yes—
257C42×C43C2412yes—
258C22⋊Dic43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261#10621885—28no—
262#10621885—44no—
263#10621883—44no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—24no—
267C4⋊Dic43—21no—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—44no—
283C2×C43⋊C8—44no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286C2×C43⋊C8C2412yes—
287C2×C43⋊C8C2412yes—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43#13514yes—
298C23×C43C22×D412yes—
299C23×C43C22×D412yes—
300C23×C43C22×D411yescharacteristic
301Q8×C43—24no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—48no—
306Q8×C43—42no—
307Q8×C43C2×#4114yes—
308D4×C43—28no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—48no—
312D4×C43—48no—
313D4×C43—42no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—24no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—24no—
321C2×C4×C43—24no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—48no—
329C2×C4×C43—48no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D412yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4112yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43C2511yescharacteristic
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—42no—
345C2×Dic43—48no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349Dic86—22no—
350Dic86—22no—
351Dic86—42no—
352C43⋊C8—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C43⋊C8—22no—
356C2×#3300—431nomaximal, Sylow
357C22×C43—22no—
358C22×C43—28no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—44no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—84no—
368C22×C43#54612yes—
369C22×C43C2×#13514yes—
370C22×C43C2×#13512yes—
371C22×C43#57812yes—
372C22×C43C23×D411yescharacteristic
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—24no—
376C4×C43—22no—
377C4×C43—22no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43#54612yes—
381C4×C43C22×#4111yescharacteristic
382C4×C43C2×H(5,𝔽2)11yescharacteristic
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387C2×#552—431no—
388C2×#548D4311yescharacteristic
389#3300—4316no—
390C2×#488—431no—
391C2×#485—431no—
392C2×#480—431no—
393C2×#479—431no—
394C2×#467—431no—
395C2×#465—431no—
396C2×#464—431no—
397C2×#452—431no—
398C2×#451—431no—
399C2×C4×Q16—431no—
400C2×C8×D4—431no—
401C2×#416—431no—
402C22×#103—431no—
403C2×C43—24no—
404C2×C43—42no—
405C2×C43—82no—
406C2×C43#330014yescomplemented
407C2×C43C2×#54611yescharacteristic
408C2×C43C22×#13511yescharacteristic
409C2×C43C2×#57811yescharacteristic
410C22×#41C2×D4311yescharacteristic
411C23×Q8C2×D4311yescharacteristic
412C22×Q16—431no—
413C22×Q16—431no—
414C22×SD16—431no—
415C23×C8—431no—
416C23×C8—431no—
417#552—438no—
418#552—864no—
419#548—24no—
420#548C2×D4318yes—
421C2×#126—861no—
422C2×#125—431no—
423C2×#125—861no—
424C2×#124—21no—
425C2×#124C2×D4311yescharacteristic
426C2×#123—861no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—431no—
430C2×C22⋊Q8C2×D4311yescharacteristic
431C2×#121—21no—
432C2×#121C2×D4311yescharacteristic
433C2×C4×Q8—431no—
434C2×C4×Q8C2×D4311yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C2×D4311yescharacteristic
437C2×#117—431no—
438C2×#117—861no—
439C22×C4⋊C4—431no—
440#488—438no—
441#485—438no—
442#480—438no—
443#479—438no—
444#467—438no—
445#465—438no—
446#464—438no—
447#452—438no—
448#451—438no—
449C4×Q16—438no—
450C8×D4—438no—
451C2×#107—431no—
452C2×#107—431no—
453C2×#106—431no—
454C2×C4⋊C8—431no—
455#416—438no—
456C2×#103—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—438no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×C22⋊C8—431no—
468C2×C22⋊C8—431no—
469C2×C4×C8—431no—
470C43C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D4314yes—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—431no—
480C22×Q8C22×D4311yescharacteristic
481C22×Q8C22×D4314yes—
482C22×Q8C22×D4311yescharacteristic
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C22⋊D4311yescharacteristic
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—861no—
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C2×Q16—434no—
493C2×Q16—434no—
494C2×Q16—864no—
495C2×Q16—1722no—
496C2×SD16—434no—
497C2×SD16—1722no—
498C22×C8—431no—
499C22×C8—431no—
500C22×C8—431no—
501C22×C8—431no—
502C22×C8—434no—
503C22×C8—434no—
504C22×C8—1722no—
505C22×C8—1722no—
506#126—868no—
507#125—434no—
508#125—868no—
509#125—862no—
510#124—28no—
511#124—22no—
512#124C22×D4314yes—
513#123—868no—
514C22⋊Q8—22no—
515C22⋊Q8—28no—
516C22⋊Q8—434no—
517C22⋊Q8—434no—
518C22⋊Q8—862no—
519C22⋊Q8—862no—
520C22⋊Q8C22×D4314yes—
521#121—28no—
522#121—22no—
523#121C22×D4314yes—
524C4×Q8—22no—
525C4×Q8—434no—
526C4×Q8—862no—
527C4×Q8C22×D4314yes—
528C4×D4—28no—
529C4×D4C22⋊D4314yes—
530C4×D4C22×D4314yes—
531#117—434no—
532#117—862no—
533#117—868no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—434no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—862no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4C22⋊D4311yescharacteristic
548C2×C4⋊C4C22×D4311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4C22⋊D4311yescharacteristic
557C2×C22⋊C4C22⋊D4311yescharacteristic
558C2×C42—21no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107—434no—
564#106—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#102—434no—
574#102—434no—
575#102—434no—
576C22⋊C8—434no—
577C22⋊C8—434no—
578C4×C8—434no—
579C24—21no—
580C24C2×C22⋊D4311yescharacteristic
581C24C2×C22⋊D4311yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—28no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—432no—
596C2×Q8—861no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8#1062190014yes—
600C2×Q8C23×D4312yes—
601C2×Q8C23×D4312yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4C2×C22⋊D4314yes—
611C2×D4C23×D4312yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—864no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—1724no—
629C22×C4C2×C22⋊D4312yes—
630C22×C4C2×C22⋊D4312yes—
631C22×C4C2×C22⋊D4311yescharacteristic
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4311yescharacteristic
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638Q16—868no—
639Q16—1724no—
640SD16—1724no—
641C2×C8—432no—
642C2×C8—432no—
643C2×C8—432no—
644C2×C8—432no—
645C2×C8—862no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8—1724no—
650C2×C8—1724no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—432no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—864no—
660C4⋊C4—861no—
661C4⋊C4—864no—
662C4⋊C4—864no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4C2×C22⋊D4314yes—
667C4⋊C4C23×D4312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C22⋊C4C2×C22⋊D4314yes—
676C22⋊C4C2×C22⋊D4314yes—
677C42—24no—
678C42—864no—
679C42—864no—
680C42C2×C22⋊D4312yes—
681C42C23×D4312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23#1306334514yes—
692C23C22×C22⋊D4312yes—
693C23C22×C22⋊D4312yes—
694C23C22×C22⋊D4311yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—42no—
701Q8—862no—
702Q8—862no—
703Q8—1722no—
704Q8C2×#1062190014yes—
705D4—28no—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—48no—
710D4—42no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—1728no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4C22×C22⋊D4312yes—
739C2×C4C22×C22⋊D4312yes—
740C2×C4C22×C22⋊D4312yes—
741C2×C4C22×C22⋊D4312yes—
742C2×C4C22×C22⋊D4311yescharacteristic
743C2×C4C2×#1062190012yes—
744C2×C4#1306337012yes—
745C2×C4C24×D4311yescharacteristic
746C8—862no—
747C8—862no—
748C8—862no—
749C8—862no—
750C22—22no—
751C22—22no—
752C22—28no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22#1458354312yes—
762C22C2×#1306334514yes—
763C22C2×#1306334512yes—
764C22#1458371412yes—
765C22C23×C22⋊D4311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4—1722no—
777C4#1458354312yes—
778C4C22×#1062190011yescharacteristic
779C4C2×#1306337011yescharacteristic
780C2—24no—
781C2—42no—
782C2—82no—
783C2#1914648214yesdirect product factor
784C2C2×#1458354311yescharacteristic
785C2C22×#1306334511yescharacteristic
786C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
Fitting, prime radicalC2×C43×#548C2
socleC23×C43C22×D4
hypercenterC2×#548D43
hypocenterC43C2×#3300
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583589C2semidirect
2. #19146482C2direct (N × H)
3. C2×#14583253C2semidirect
4. C2×#14583237C2semidirect
5. C2×#14583210C2semidirect
6. C2×#14583206C2semidirect
7. C2×#14583138C2semidirect
8. C2×#14583126C2semidirect
9. C2×#14583118C2semidirect
10. C2×#14583061C2semidirect
11. C2×#14583055C2semidirect
12. C2×C4×#10621885C2semidirect
13. C2×D4×C43⋊C8C2semidirect
14. C2×#14582895C2semidirect
15. C22×#13063249C2semidirect
23. #14583589C22semidirect
34. #14583253C22semidirect
35. #14583237C22semidirect
36. #14583210C22semidirect
37. #14583206C22semidirect
38. #14583138C22semidirect
39. #14583126C22semidirect
40. #14583118C22semidirect
41. #14583061C22semidirect
42. #14583055C22semidirect
43. C4×#10621885C22semidirect
44. D4×C43⋊C8C22semidirect
49. #14582895C22semidirect
56. C2×#13063249C22semidirect
406. C2×C43#3300semidirect
470. C43C2×#3300semidirect
783. C2#19146482direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145835892
#191464822
C2×#145832532
C2×#145832372
C2×#145832102
C2×#145832062
C2×#145831382
C2×#145831262
C2×#145831182
C2×#145830612
C2×#145830552
C2×C4×#106218852
C2×D4×C43⋊C82
C2×#145828952
C22×#130632492
C2×C43×#5482
C2×#330043